We present a characterization for positive definite operator-valued kernel to be universal or [Formula: see text]-universal, and apply these characterizations family of kernels that are shown well behaved. Later, we obtain an differentiable text]-universal text]-universal. In order such examples, generalize some well-known results concerning the structure context. On examples is given emphasis ...

This paper considers strongly continuous semigroups of operators on Banach lattices which are locally eventually positive, a property that was first investigated in the context concrete fourth-order evolution equations. We construct simple example to show typical assumptions spectrum semigroup generator considered currently literature far from necessary more general setting local eventual posit...